SOLUTION: What is an equation of a quadratic function that has zero's at -3 and 5 and has a y-intercept at (0,30)?

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Question 926572: What is an equation of a quadratic function that has zero's at -3 and 5 and has a y-intercept at (0,30)?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a quadratic function that has zero's at x%5B1%5D=-3 and x%5B2%5D=5+ and y-intercept at (0,30)
y=ax%5E2%2Bbx%2Bc...(0,30)=>c=30

y=ax%5E2%2Bbx%2B30 if x%5B1%5D=-3=>y=0
0=a%28-3%29%5E2%2Bb%28-3%29%2B30
0=9a-3b%2B30...reduce, divide by 3
0=3a-b%2B10....eq.1

y=ax%5E2%2Bbx%2B30 if x%5B1%5D=5=>y=0
0=a%285%29%5E2%2Bb%285%29%2B30
0=25a%2B5b%2B30...reduce, divide by 5
0=5a%2Bb%2B6....eq.2

solve the system:
0=3a-b%2B10....eq.1
0=5a%2Bb%2B6....eq.2
_______________________add both
0=3a-cross%28b%29%2B10%2B5a%2Bcross%28b%29%2B6
0=3a%2B10%2B5a%2B6
0=8a%2B16
-16=8a
highlight%28-2=a%29

plug it in eq.1 or 2 and find b
0=3%28-2%29-b%2B10....eq.1
b=-6%2B10
highlight%28b=4%29
so, your equation is: y=-2x%5E2%2B4x%2B30